Ecological space (ES), including forest ecological space (FES) and grassland ecological space (GES) in this study, is the land with natural attributes and the main functions of providing ecological services, which has a huge potential capacity for carbon sink (CS). The interannual fluctuation of the CS in ES is severe, which is affected by factors such as precipitation and temperature, but it is still controversial which is the dominant factor in affecting the fluctuation process of the CS in ES. To this end, the multi-source remote sensing monitoring data on the fine-grid scale were collected in this study, including the land use and land cover remote sensing monitoring data, the data products of moderate-resolution imaging spectroradiometer (including land surface water index, photosynthetically active radiation, enhanced vegetation index, gross primary productivity), and meteorological data (including precipitation and temperature). By coupling the vegetation photosynthesis model and soil respiration model, the CS in CES from 2010 to 2020 was calculated, and the interannual fluctuation trends and stability of CS in CES were analyzed. Furthermore, the correlation coefficient and partial correlation coefficient equation between the CS of CES with precipitation and temperature were constructed to explore the correlation between interannual fluctuation of CS in CES with meteorological factor, and to determine the dominant position of precipitation and temperature in affecting the fluctuation process of the CS in CES. The research results show that the annual average CS of per unit area in CES was 233.78 gC·m−2·a−1, and the cumulative CS was 11.83 PgC. The GES and FES contributed 6.33 PgC and 5.49 PgC of CS, respectively. From 2010 to 2020, the CS of CES showed an upward trend and was generally in a relatively stable state (the mean value of the coefficient of variation was 0.6248). However, the year with severe fluctuation of was found in this study (from 2013 to 2015), the reason is that the precipitation was too low in 2014, which indicated that climate change, especially the change of precipitation, played a important role in the fluctuation of CS in CES. The results of correlation analysis confirmed the above analysis. The change of CS in CES is highly positively correlated with the change of precipitation (the correlation coefficient is 0.085), and weakly positively correlation with temperature (the correlation coefficient was 0.026). The precipitation is the dominant influencing factor, which has a positive effect on CS in CES. Within a climate environment dominated by precipitation, precipitation and temperature jointly affect the CS in CES. It should be noted that in some regions with variable climate, precipitation and temperature had relatively little impact on CS in CES. Their fluctuations may depend more on the ecosystem’s own ecological services’ regulation ability and their response degree to changes in atmospheric CO2 concentration.